# Stability of Image-Reconstruction Algorithms

arXiv: https://arxiv.org/abs/2206.07128 · HTML: https://mlsanity.com/paper/2206.07128/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 65 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Measuring Robustness in Deep Learning Based Compressive Sensing](https://mlsanity.com/paper/2102.06103/) (2021)
- [Understanding neural networks with reproducing kernel Banach spaces](https://mlsanity.com/paper/2109.09710/) (2021)
- [A representer theorem for deep neural networks](https://mlsanity.com/paper/1802.09210/) (2018)
- [Stabilizing Invertible Neural Networks Using Mixture Models](https://mlsanity.com/paper/2009.02994/) (2020)
- [Sparsity of solutions for variational inverse problems with finite-dimensional data](https://mlsanity.com/paper/1809.05045/) (2018)
- [On Representer Theorems and Convex Regularization](https://mlsanity.com/paper/1806.09810/) (2018)
- [A unifying representer theorem for inverse problems and machine learning](https://mlsanity.com/paper/1903.00687/) (2019)
- [Convex Optimization in Sums of Banach Spaces](https://mlsanity.com/paper/2104.13127/) (2021)
- [Indirect Image Registration with Large Diffeomorphic Deformations](https://mlsanity.com/paper/1706.04048/) (2017)
- [Template-Based Image Reconstruction from Sparse Tomographic Data](https://mlsanity.com/paper/1810.08596/) (2018)
- [Exact solutions of infinite dimensional total-variation regularized problems](https://mlsanity.com/paper/1708.02157/) (2017)
- [Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity-Part II: Proximal Optimization and Performance Evaluation](https://mlsanity.com/paper/1710.01622/) (2017)
- [A unified approach to convergence rates for ℓ1-regularization and lacking sparsity](https://mlsanity.com/paper/1506.01582/) (2015)
- [Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity-Part I: Modeling and Inverse Problems](https://mlsanity.com/paper/1710.01604/) (2017)
- [SpotNet - Learned iterations for cell detection in image-based immunoassays](https://mlsanity.com/paper/1810.06132/) (2018)

## Built on by (most cited first, 7 of 7)

- [Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems](https://mlsanity.com/paper/2303.15845/) (2023)
- [Stability of Data-Dependent Ridge-Regularization for Inverse Problems](https://mlsanity.com/paper/2406.12289/) (2024)
- [Iteratively Refined Image Reconstruction with Learned Attentive Regularizers](https://mlsanity.com/paper/2407.06608/) (2024)
- [Parseval Convolution Operators and Neural Networks](https://mlsanity.com/paper/2408.09981/) (2024)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizers](https://mlsanity.com/paper/2503.19190/) (2025)
- [Triggering hallucinations in model-based MRI reconstruction via adversarial perturbations](https://mlsanity.com/paper/2602.18536/) (2026)

## Abstract (arXiv)

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies (ℓ2 and ℓ1 regularization) and present novel stability results for ℓp-regularized linear inverse problems for p∈(1,∞). Our results guarantee Lipschitz continuity for small p and H"older continuity for larger p. They generalize well to the Lp(Omega) function spaces.